In a small bowl, stir together the mayonnaise, sun-dried tomato tomato pesto and lemon juice. Cover and refrigerate until serving.
In a large bowl, whisk together vinegar, oil, garlic, mustard, salt & pepper.
Add mushrooms, onions & peppers, turning to coat with the marinade.
Remove vegetables from the marinade, letting any excess drip off. Reserve the marinade. Grill the vegetables until browned on both sides and tender, about 5 minutes per side, brushing once with additional marinade during cooking.
Meanwhile, toast the rolls at the edge of the grill or in a toaster.
To assemble, divide arugula among the 4 roll bottoms. Top with onions & peppers. Set the mushroom caps on top. Spread 1/4 of the mayo on each roll top and set on top of the mushrooms.
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